The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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DERIVED FUNCTOR COHOMOLOGY GROUPS WITH YONEDA PRODUCT

  • Husain, Hafiz Syed (Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology) ;
  • Sultana, Mariam (Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology)
  • Received : 2020.05.31
  • Accepted : 2021.05.06
  • Published : 2021.05.31
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Abstract

This work presents an exposition of both the internal structure of derived category of an abelian category D*(𝓐) and its contribution in solving problems, particularly in algebraic geometry. Calculation of some morphisms will be presented between objects in D*(𝓐) as elements in appropriate cohomology groups along with their compositions with the help of Yoneda construction under the assumption that the homological dimension of D*(𝓐) is greater than or equal to 2. These computational settings will then be considered under sheaf cohomological context with a particular case from projective geometry.

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Acknowledgement

The referees have reviewed the paper very carefully. The authors express their deep thanks for the comments.

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